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WASHINGTON — Arkansas Senator Blanche Lincoln barely beat back a Democratic primary challenge last night and Tea Party movement candidate Sharron Angle scored a stunning victory in Nevada’s GOP Senate primary, as voters across the country sent a message that established politicians are endangered this election season.

Angle, who wants to scrap the Department of Education, phase out Social Security, and dump nuclear waste at Nevada’s Yucca Mountain, benefited from a late surge among antiestablishment voters and outside cash from groups demanding a more conservative voice in the Silver State. She will face the top GOP target this November: Senate majority leader Harry Reid.

Lincoln, forced into a runoff election against Lieutenant Governor Bill Halter, had been targeted by labor unions and liberal organizations angry with the moderate lawmaker’s opposition to the public option in the health care law, a provision that failed in part because of Lincoln’s vote. As yesterday’s primary approached, many Democratic observers had prepared her political obituary as Halter overtook her in the polls.

Outside organizations had dumped millions of dollars into the Arkansas race to support Halter. But Arkansans sent a message last night, a relieved and ebullient Lincoln told supporters.

“That message was that the vote of this senator is not for sale, and neither is the vote of the people of Arkansas,’’ she said.

Lincoln still faces a tough challenge this fall from the GOP nominee, John Boozman, a congressman.

Her brutal struggle for renomination underscored the battles that entrenched candidates face this election year.

Representative Bob Inglis, a six-term Republican, barely garnered enough votes last night to force a runoff in South Carolina.

And Governor Jim Gibbons of Nevada, an incumbent damaged by details of an extramarital affair disclosed during a nasty divorce, was soundly defeated in his GOP bid for renomination. It was the first time a Nevada governor was beaten in his own primary.

Incumbency has historically been a powerful advantage for candidates, especially in primary elections. But the political calculus has changed this year as voters demand something and often someone new.

“Incumbents are just reviled,’’ said Peter Fenn, a Democratic consultant based in Washington, D.C. “If you’re in power, you’re in trouble.’’

Last month, veteran Senator Arlen Specter of Pennsylvania was defeated in his Democratic primary by Representative Joe Sestak, while Senator Bob Bennett, Republican of Utah, was defeated in his party’s nomination process. Rand Paul, backed by the Tea Party movement, won the Republican nomination for Senate in Kentucky, easily besting an opponent widely endorsed by the GOP establishment.

The Tea Party movement racked up several victories last night. Paul LePage, the mayor of Waterville, won the GOP gubernatorial primary in Maine and will face Democratic nominee Libby Mitchell. In Georgia, Tom Graves rode his association with the Atlanta Tea Party Patriots to victory over fellow conservative Lee Hawkins in a special election for the congressional seat vacated by Nathan Deal. Graves becomes the first Tea Party movement candidate this year to be elected to Congress.

The votes were part of a slew of coast-to-coast primaries yesterday in 12 states, encompassing 20 percent of the nation’s voters.

One of the most closely watched races nationally was the Senate primary in Nevada. Republicans backed Angle over state GOP former chair Sue Lowden, even though Angle’s stances could alienate independent moderate voters in the race to defeat Reid. Her win concerns some GOP leaders and delights Democrats in Nevada, analysts said.

“This is a state with the biggest prize on the Republican side,’’ said David Demore, a political science professor at the University of Nevada, Las Vegas. Demore agreed that her win could boost Reid’s chances.

The embattled Senate leader is considered extremely vulnerable in the conservative-leaning state because of his support for President Obama and his stature as a cornerstone of the Washington establishment. A Reid defeat in November would not only boost GOP ranks, but would deliver a devastating psychological blow to Democrats, Demore said.

The Nevada primary had been considered a key gauge of how much support the emerging Tea Party movement has among disgruntled voters and how much influence it has in the GOP.

Lowden had been the front-runner until last month and was considered a strong candidate to beat Reid. Democrats consider Angle, a former state legislator known for often-lone antitax crusades, an easier opponent.

“I think they’re as happy as anyone with a 38 percent approval rating can be,’’ said Nevada-based political analyst Jon Ralston, describing the Reid camp’s reaction to Angle’s popularity.

In South Carolina, Republicans struggled to overcome a potential sex scandal. Nikki Haley had been the leading GOP contender heading into the primary to replace Governor Mark Sanford, whose tenure was derailed by an affair with an Argentinian woman and his attempt to cover it up.

But Haley herself has been accused of extramarital affairs, a charge she denies. Last night, she grabbed about 49 percent of the vote, not enough to prevent a runoff against the second-place finisher, Representative Gresham Barrett.

In California, Republicans nominated female business executives to vie for both governor and the Senate.

Former Hewlett-Packard chief executive Carly Fiorina will face Democratic incumbent Barbara Boxer for the US Senate and former eBay executive Meg Whitman will face Democrat Jerry Brown for the governorship he once held.

“A lot of what’s going down in the country is really an anti-incumbent attitude and ire,’’ said Eric Baker, a political science professor at University of Arkansas at Fort Smith.

“A lot of the anger is really not ideological; it’s anger against the system.’’

Correction: Because of a reporting error, a story in yesterday's Nation pages in later editions misidentified the offices sought by Carly Fiorina and Meg Whitman in California. Fiorina will face Democratic incumbent Barbara Boxer for the US Senate; Whitman will face Jerry Brown for governor.